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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 52 Issue: 2

Statistical $\rho$-commutative algebras

Zahra Bagheri(Arak University)0000-0002-5821-8999
Esmaeil Peyghan(Arak University)0000-0002-2713-6253
Sayfa
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Yayın Tarihi
2023-03-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Then by recalling the notions of almost (para-)Kähler $\rho$-commutative algebras, we generalized the notion of Codazzi-(para-)Kähler $\rho$-commutative algebra as a (para-)Kähler (or Fedosov) $\rho$-commutative algebra which is at the same time statistical and moreover define the holomorphic $\rho$-commutative algebras.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this article, we study Codazzi-couples of an arbitrary connection $\nabla$ with a nondegenerate 2-form $\omega$, an isomorphism $L$ on the space of derivation of $\rho$-commutative algebra $A$, which the important examples of isomorphism $L$ are almost complex and almost para-complex structures, a metric $g$ that $(g, \omega,L)$ form a compatible triple.
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Temel Bulgular & Veri:We study a statistical structure on $\rho$-commutative algebras by the classical manner on Riemannian manifolds.
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Sonuç & Katkı:Then by recalling the notions of almost (para-)Kähler $\rho$-commutative algebras, we generalized the notion of Codazzi-(para-)Kähler $\rho$-commutative algebra as a (para-)Kähler (or Fedosov) $\rho$-commutative algebra which is at the same time statistical and moreover define the holomorphic $\rho$-commutative algebras.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:statistical structure · Codazzi-couple · Kähle structure

Abstract

In this article, we study Codazzi-couples of an arbitrary connection $\nabla$ with a nondegenerate 2-form $\omega$, an isomorphism $L$ on the space of derivation of $\rho$-commutative algebra $A$, which the important examples of isomorphism $L$ are almost complex and almost para-complex structures, a metric $g$ that $(g, \omega,L)$ form a compatible triple. We study a statistical structure on $\rho$-commutative algebras by the classical manner on Riemannian manifolds. Then by recalling the notions of almost (para-)Kähler $\rho$-commutative algebras, we generalized the notion of Codazzi-(para-)Kähler $\rho$-commutative algebra as a (para-)Kähler (or Fedosov) $\rho$-commutative algebra which is at the same time statistical and moreover define the holomorphic $\rho$-commutative algebras.

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Bu Makaleye Atıf Yap

Bagheri, Z., Peyghan, E. (2023). Statistical $\rho$-commutative algebras. Hacettepe Journal of Mathematics and Statistics, Volume: 52 Issue: 2. https://doi.org/10.15672/hujms.1105421

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Kaynakça (21)

  1. S. Amari and H. Nagaoka, Methods of information geometry, in: Transl. Math. Monogr., Amer. Math. Soc. 191, 2000.
  2. Z. Bagheri and E. Peyghan, (Para-) Kähler structures on $\rho$-commutative algebras, Adv. Appl. Clifford Algebras 28 (5), 95, 2018.
  3. P. J. Bongaarts and H. G. J. Pijls, Almost commutative algebra and differential calculus on the quantum hyperplane, J. Math. Phys. 35 (2), 959–970, 1994.
  4. S.Y. Cheng and S. T. Yau, The real Monge-Amp‘ere equation and affine flat structures. In: Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, Vol. I, Science Press, New York, 339-370, 1982.
  5. C. Ciupala, Linear connections on almost commutative algebras, Acta. Th. Univ. Comenianiae 72 (2), 197207, 2003.
  6. C. Ciupala, Connections and distributions on quantum hyperplane, Czech. J. Phys. 54 (8), 921–932, 2004.
  7. C. Ciupala, 2-$\rho$-derivation on a $\rho$-algebra and application to the quaternionic algebra, Int. J. Geom. Meth. Mod. Phys. 4 (3), 457–469, 2007.
  8. M. Dubois-Violette, Dérivations et calcul différentiel non commutatif, C.R. Acad. Sci. Paris, série I. 307, 403–408, 1988.
  9. T. Fei and J. Zhang, Interaction of Codazzi Couplings with (Para-)Kähler Geometry, Results Math. 72 (2), 2017. DOI 10.1007/s00025-017-0711-7.
  10. H. Furuhata and I. Hasegawa, Submanifold theory in holomorphic statistical manifolds, in: S. Dragomir, M.H. Shahid, F.R. Al-Solamy (Eds.), Geometry of Cauchy- Riemann Submanifolds, Springer, Singapore, 179–215, 2016.
  11. E. Kähler, Über eine bemerkenswerte Hermtesche metrik, Abn. Sem. Unv. Hamburg 9, 173–186, 1933.
  12. S. L. Lauritzen, Statistical manifolds, In: Differential Geometry in Statistical Inferences, IMS Lecture Notes Monogr. Ser., 10, Inst. Math. Statist., Hayward California, 96–163, 1987.
  13. S. Majid, Classification of bicovariant differential calculi, J. Geom. Phys. 25, 119–140, 1998.
  14. S. Majid, Riemannian geometry of quantum groups and finite groups with nonuniversal differentials, Commun. Math. Phys. 225, 131–170, 2002.
  15. F. Ngakeu, Levi-Civita connection on almost commutative algebras, Int. J. Geom. Meth. Mod Phys. 4 (7), 1075–1085, 2007.
  16. F. Ngakeu, S. Majid and D. Lambert, Noncommutative Riemannian geometry of the alternating group A4, J. Geom. Phys. 42, 259–282, 2002.
  17. K. Nomizu and T. Sasaki,Affine Differential Geometry: Geometry of Affine Immersions, Volume 111 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1994.
  18. H. Shima, On certain locally flat homogeneous manifolds of solvable Lie groups, Osaka J. Math. 13 (2), 213-229, 1976.
  19. U. Simon, Affine differential geometry. In: Dillen, F., Verstraelen, L. (eds.) Handbook of Differential Geometry, North-Holland 1, 905–961, 2000.
  20. K.Takano, Statistical manifolds with almost complex structures and its statistical submersions, Tensor N.S. 65, 128–142, 2004.
  21. K.Takano, Statistical manifolds with almost contact structures and its statistical submersions, J. Geom. 85, 171–187, 2006.